Beta hedging with options?

How do you beta hedge with two options that have different underliers? In other words, how would one reproduct a typical long/short pair-trade with options?

Let's say you are going to buy AAPL 1month Calls 5% OTM, and you want to hedge it by buying SPY's puts: How would you think about the appropriate strike px for the puts? How would youadjust for the different volatility of both underliers, and what are other considerations that should be thought about?

Comments (5)

Most Helpful
Nov 11, 2018

First, think of what is the general view you are making. It's "Apple will outperform S&P", right? However, the exact nature of that view will determine how you want to structure the trade, since by trading options you are adding a dimension.

If you are forecasting that AAPL is going to outperform the index on the way up, then you can create a conditional spread by buying a call on AAPL and selling a call on the index to finance is. In that case you can use some form of break-even logic and your thinking would be something like "I am long Apple which has a beta of 1.2 to Nasdaq, so if I sell 1.2 units of NDX options, what moneyness can I get?"

Alternatively, you can be saying If you are like to be long AAPL but you don't like to be long the market. In that case, you just buy an Apple call and sell the futures against it's delta (i.e. delta * beta). Buying puts against your calls kinda doubles up on that view, so it's not necessary.

Finally, buying a call on one and a put on the other expresses a view that you think Apple will be outperforming the market rain or shine, but want to have some convexity to play it. A a collateral view, you think both market and street vol is cheap (really?). In that case, you probably want to put on the initial structure delta*beta neutral but do not adjust your deltas as they change.

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Nov 11, 2018

Re-reading my scribbles makes me think that (a) I should have taken an English writing class when I had the chance and (b) I should be on Adderall to avoid making careless mistakes

Nov 14, 2018
Mostly Random Dude:

Alternatively, you can be saying If you are like to be long AAPL but you don't like to be long the market. In that case, you just buy an Apple call and sell the futures against it's delta (i.e. delta * beta). Buying puts against your calls kinda doubles up on that view, so it's not necessary.

Thanks for your help. A few questions...
1. Is it necessary to have to take a view on the way that AAPL will outperform the NDX up to the expiry date? -- can we instead just have a view on where these two will be at whatever expiration date? (Does that default to mean that generally, we would expect APPL to outperform the NDX up to the expiry?)

  1. I'm not sure what you mean by selling futures against it's delta? Does this mean selling puts? Against the delta? ---and then you go on to say that buying puts against the calls would double up on this view? Are you saying that buying puts against calls would double up on the view IF we already had "sold futures against it's delta"? If so, then what about just buying puts against the calls from the onset, as I had originally suggested? We wouldn't be 'doubled up' then?...

Thanks for your help

Nov 11, 2018
Capital Returns:

1. Is it necessary to have to take a view on the way that AAPL will outperform the NDX up to the expiry date? -- can we instead just have a view on where these two will be at whatever expiration date? (Does that default to mean that generally, we would expect APPL to outperform the NDX up to the expiry?)

The general principle is that if you are thinking about the options delta, you are playing current moves vs if you are thinking it terms of notional amount you considering returns at expiration. So in 1 your view is that on expiration date return of APPL will be higher than return of your index hedge times whatever beta you used.

Capital Returns:

2. I'm not sure what you mean by selling futures against it's delta? Does this mean selling puts? Against the delta? ---and then you go on to say that buying puts against the calls would double up on this view? Are you saying that buying puts against calls would double up on the view IF we already had "sold futures against it's delta"? If so, then what about just buying puts against the calls from the onset, as I had originally suggested? We wouldn't be 'doubled up' then?...

You buy a call on AAPL. It has some $ delta (i.e. how does the price of the options change for every dollar in underlying). To hedge out the market risk, you sell NQ futures in the amount equal to delta * beta. You don't want to trade puts because you already long convexity on AAPL which is a combination of market risk and idiosyncratic risk. Depending on the strike this could be a neutral or a market-bullish view, such as you make more money if market rallies and AAPL outperforms.

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Nov 14, 2018